Sensitivity analysis for strongly nonlinear quasi-variational inclusions

Existence and algorithm of solutions for a new system of generalised variational inclusions involving relaxed Lipschitz mappings

“…Also, (14) implies that {y n } is a Cauchy sequence in H. Hence, there exist x, y ∈ H such that x n → x and y n → y . Since g, A, S, B, T, J ρ M and J γ N are continuous, then it follows from Algorithm 1 that x, y ∈ H satisfy (3), (4) and thus by Lemma 2, it follows that x, y ∈ H is a solution of system of generalized variational inclusions (1). This completes the proof.…”

“…Because of applications in mechanics, physics, optimization and control, nonlinear programming, economics and engineering sciences, various variational inclusions have been intensively studied in recent years by Agarwal [1,2], Ahmad et al [5], Ding et al [7] and Lee et al [8]. Ansari and Yao [4] studied a system of variational inequalities using a fixed point theorem.…”

Generalized nonlinear implicit quasivariational inclusions

“…As in the proof of (4.10), we have (2) if n = α n ∆ n + γ n with ∞ n=0 γ n < +∞ and lim n→∞ ∆ n = 0, then lim n→∞ y n = u * , (3) lim n→∞ y n = u * implies that lim n→∞ n = 0.…”

“…A useful and important generalization of variational inequalities is a variational inclusion. Using the resolvent operator technique, many authors have studied various variational inequalities and inclusions with applications (see [1,2,5,6,8,9,10,11,12,13,14,16,18,19,20,21] and the references therein).…”

Sensitivity Analysis for System of Parametric Generalized Quasi-Variational Inclusions Involving R-Accretive Mappings

“…By using the implicit function approach that makes use of so-called normal mappings, Robinson [35] studied the sensitivity analysis of solutions for variational inequalities in finite-dimensional spaces. By using proximal-point mappings technique, Adly [1], Noor [35] and Agarwal et al [2] studied the sensitivity analysis of solution set of some classes of quasi-variational inclusions involving single-valued mappings. By using projection and proximal-point mappings techniques, Ding and Luo [15], Liu et al [26], Park and Jeong [32], Ding [14], and Kazmi and Khan [23,24], studied the behavior and sensitivity analysis of solution set for some classes of generalized variational inequalities (inclusions) involving set-valued mappings.…”